Grade 10 · Math · Geometry

10th grade Which angle pairs prove that two lines are parallel? worksheet

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Which angle pairs prove that two lines are parallel?

Grade 10 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Luz draws two lines on paper. m∠DGH = (3x + 5)° and m∠GHQ = (2x + 25)°. What value of x makes DF ∥ QS?
Milo checks two bike lanes. m∠UGF = (4x − 10)° and m∠SHV = (x + 35)°. What value of x makes DF ∥ QS?
Use the picture in question 1.
Noah checks two stripes on a rug. m∠FGH = (6x + 4)° and m∠GHS = (2x + 16)°. What value of x makes DF ∥ QS?
Use the picture in question 1.
Pia draws two lines in crayon. m∠UGD = (5x − 4)° and m∠QHV = (3x + 8)°. What value of x makes DF ∥ QS?
Use the picture in question 1.
Ari's rug is quadrilateral PQRS with PQ ∥ SR and PS ∥ QR. Diagonal PR has m∠QPR = 25° and m∠PRQ = 52°. What is m∠P?
Bo's map tile is quadrilateral PQRS with PQ ∥ SR and PS ∥ QR. Diagonal PR has m∠QPR = 33° and m∠PRQ = 49°. What is m∠S?
Use the picture in question 5.
Esme's paper is quadrilateral PQRS with PQ ∥ SR and PS ∥ QR. Diagonal PR has m∠QPR = 36° and m∠PRQ = 44°. SR is extended past R to T. What is m∠QRT?
Use the picture in question 5.
8.
Jun measures corresponding angles where line t crosses lines l, m and n: 68° at l, 68° at m and 71° at n. Which statement is justified?
- No two lines are parallel: corresponding angles must add to 180°, and 68° + 68° does not equal 180°
- m ∥ n, since their angles, 68° and 71°, differ by just 3°, which is close enough to be equal
- l ∥ n, since 71° at n and its supplement 109° add to 180°, which is the test for parallel lines
- l ∥ m, since their corresponding angles are both 68°, while n is parallel to neither
9.
Kira can use one given to prove DF ∥ QS. Which given is enough?
- m∠FGH = 112° and m∠GHS = 112°, same-side interior angles that are congruent
- m∠DGH = 68° and m∠GHS = 112°, alternate interior angles that add to 180°
- m∠FGH = 112° and m∠GHQ = 112°, alternate interior angles that are congruent
- m∠UGF = 72° and m∠FGH = 108°, a linear pair that adds to 180°
10.
Milo writes: m∠UGF + m∠GHS = 180°, so by the converse of the Same-Side Interior Angles Theorem, DF ∥ QS. What is wrong?
Use the picture in question 9.
- ∠UGF and ∠GHS are corresponding angles, and the converse for them needs them to be congruent, not supplementary
- Nothing is wrong: angles at the two crossings that add to 180° make the lines parallel
- The name is wrong: the proof should cite the converse of the Alternate Interior Angles Theorem
- The sum is wrong: for parallel lines these two angles add to 360°, so the test fails

10th grade Which angle pairs prove that two lines are parallel? worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Proving lines parallel. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can decide from two angle measures whether two lines are parallel, and say which rule decides it.
I can choose a fact, and the converse that goes with it, that proves two lines parallel.
I can find the value of x that makes two lines parallel, give the reason for a step in a proof, name a missing step, and find an angle across two pairs of parallel sides.

Standard: G-CO.C.9 (converses; related, the CCSS text names the forward theorems)

Words to know

converse: The if-then rule turned around: "if the angles are equal, then the lines are parallel".

prove parallel: Show from angles that two lines never meet.

one crossing: The angles around G only (or H only); facts there hold for any lines.

not to scale: The sketch's look does not count; only the numbers do.

Common mistakes

Your child expected equal pairs (corresponding or alternate angles) to add to 180°.

Your child expected same-side angles to be equal; for parallel lines they add to 180°.

Your child decided from how the sketch looks.

What to say

Ask: for parallel lines, which pairs match in size?

Ask: is one angle wide and the other narrow?

Ask: does the sketch say it is drawn to scale?

Questions parents ask

What is the most common mistake with which angle pairs prove that two lines are parallel??

Your child expected equal pairs (corresponding or alternate angles) to add to 180°.

How can I help my child with which angle pairs prove that two lines are parallel??

Ask: for parallel lines, which pairs match in size?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

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